In the given figure ps=pt, pq =pr and angle qpr = angle spt. prove tha

1.	In the given figure ps=pt, pq =pr and angle qpr = angle spt. prove that qs=rt.plz answer guysI will mark best as brainliest
Answer» Step-by-step EXPLANATION: In the given FIGURE, we are provided that, PS = PT PQ = PR also, ∠QPR = ∠SPT As we know that Angle opposite to the equal sides are also equal. Therefore, ∠PQR = ∠PRQ = θ (say) (because, PQ = PR) also, ∠PST = ∠PTS = ∅ (say) (because, PS = PT) Now, As, Sum of angles in a TRIANGLE is equal to 180°. Therefore, in triangle PQR, ∠QPR = 180° - ∠PQR - ∠PRQ = 180° - θ - θ = 180° - 2θ Similarly, in triangle PST, ∠TPS = 180° - ∠PST - ∠PTS = 180° - ∅ - ∅ = 180° - 2∅ But, ∠QPR = ∠TPS (given) So, 180° - 2θ = 180° - 2∅ θ = ∅ Now, In triangle PQS and triangle PRT, PQ = PR (given) ∠QPS = 180° - 2θ + ∠RPS = ∠TPR = 180° - 2∅ + ∠RPS (because, θ = ∅) and, PS = PT (given) Therefore, Triangle PQS ≅ Triangle PRT (SAS congruency) So, QS = RT HENCE, proved.

In the given figure ps=pt, pq =pr and angle qpr = angle spt. prove that qs=rt.plz answer guysI will mark best as brainliest

Answer»

Step-by-step EXPLANATION:

In the given FIGURE, we are provided that,

PS = PT

PQ = PR

also,

∠QPR = ∠SPT

As we know that Angle opposite to the equal sides are also equal.

Therefore,

∠PQR = ∠PRQ = θ (say) (because, PQ = PR)

also,

∠PST = ∠PTS = ∅ (say) (because, PS = PT)

Now,

As,

Sum of angles in a TRIANGLE is equal to 180°.

Therefore, in triangle PQR,

∠QPR = 180° - ∠PQR - ∠PRQ = 180° - θ - θ = 180° - 2θ

Similarly, in triangle PST,

∠TPS = 180° - ∠PST - ∠PTS = 180° - ∅ - ∅ = 180° - 2∅

But,

∠QPR = ∠TPS (given)

So,

180° - 2θ = 180° - 2∅

θ = ∅

Now,

In triangle PQS and triangle PRT,

PQ = PR (given)

∠QPS = 180° - 2θ + ∠RPS = ∠TPR = 180° - 2∅ + ∠RPS (because, θ = ∅)

and,

PS = PT (given)

Therefore,

Triangle PQS ≅ Triangle PRT (SAS congruency)

So,

QS = RT

HENCE, proved.